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Transparent Boundary Conditions for Elastic Anisotropic VTI Media: Axially Symmetric Case

Published online by Cambridge University Press:  20 August 2015

Olga Podgornova
Olga Podgornova*
Affiliation:
Schlumberger Moscow Research, 13, Pudovkina, 119285, Russia
*
*Corresponding author.Email:[email protected]
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Abstract

Transparent boundary conditions (TBCs) for anisotropic vertical transverse isotropic VTI medium are formulated for the axially symmetric case. The high accuracy of the derived TBCs and their long-time stability are demonstrated in numerical experiments. The TBCs are represented in terms of the vertical component of the velocity vector and tangential component of the stress tensor that facilitates the easy implementation of the boundary condition into the finite-difference staggered-grid scheme.

Keywords

65M9935L0530E1074E1074B05Nonreflecting boundary conditionsanisotropy elastodynamics
Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 2 , February 2012 , pp. 541 - 554
Copyright
Copyright © Global Science Press Limited 2012

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References

[1]Alpert, B., Greengard, L., and Hagstrom, T.. Nonreflecting boundary conditions for the time-dependent wave equation. J. Comput. Phys., 180:270–296, 2002.Google Scholar
[2]Becache, E., Fauqueux, S., and Joly, P.. Stability of Perfectly Matched Layers, Group Velocities and Anisotropic Waves, J. Comput. Phys., 188(2):399–433, 2003.CrossRefGoogle Scholar
[3]Berenger, J.P.. A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys., 114:185–200, 1994.Google Scholar
[4]Hagstrom, T., and Lau, S.. Radiation boundary conditions for Maxwells equations: A review of accurate time-domain formulations. J. Comput. Math., 25:305–336, 2007.Google Scholar
[5]Lisitsa, V., and Lys, E.. Reflectionless truncation of target area for axially symmetric anisotropic elasticity. J. Comput. Appl. Math., doi:10.1016/j.cam.2009.08.031, 2009Google Scholar
[6]Meza-Fajardo, K.C. and Papageorgiou, A.S.. A nonconvolutional, split-field, perfectly matched layer for wave propagation in isotropic and anisotropic elastic media; stability analysis. Bull. Seism. Soc. Am., 98(4):1811–1836, 2008.Google Scholar
[7]Sofronov, I.. Artificial boundary conditions of absolute transparency for two and three-dimensional external time-dependent scattering problems. Eu. J. Appl. Math., 9(6):561–588, 1998.Google Scholar
[8]Sofronov, I.. Nonreflecting inflow and outflow in wind tunnel for transonic time-accurate simulation. J. Math. Anal. Appl., 221:92–115, 1998.CrossRefGoogle Scholar
[9]Sofronov, I.L., and Zaitsev, N.A.. Numerical generation of transparent boundary conditions on the side surface of a vertical transverse isotropic layer. J. Comput. Appl. Math., 234:1732–1738, 2010.Google Scholar
[10]Thomsen, S.. Weak elastic anisotropy. Geophysics, 51(10):1954–1966, 1986.Google Scholar
[11]Tsynkov, S.V.. Numerical solution of problems on unbounded domains. A review. Appl. Numer. Math., 27(4):465–532, 1998.Google Scholar
[12]Virieux, J.. P-SV wave propagation in heterogeneous media: Velocity-stress finite-difference method. Geophysics, 51(4):889–901, 1986.Google Scholar